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Angles

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CONTENTS

ITEM TYPE NUMBER
Working with angles Workout 51 slides
Angles Library 16 questions
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SAMPLE FROM THE WORKOUT

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SLIDE 1 - QUESTION 1

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SLIDE 2 - SOLUTION

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

194: Geometry in three dimensions
216: Ratio and proportion
line
220: Angles
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222: Visual reasoning

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CONCEPTS

ITEM
 LEV.
Using angle sum of circle is 360 to find unknown angle 464.1
Semicircle 464.7
Diameter 464.7
Using angle sum of line is 180 to find unknown angle 464.8
Using right-angle is 90 to find unknown angle 465.0
acute, right-angle, obtuse and reflex angles 465.4
Angle sum of triangle = 180 degrees 465.7
Triangle problem 465.9
Angles in isosceles and equilateral triangles, base angle 466.4
Vertically opposite angles 467.4
Corresponding angles 467.6
Alternating angles 467.8
Exterior and interior angle of regular polygon 468.6

RAW CONTENT OF THE WORKOUT

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SLIDE 1 Use a protractor to measure the angles of the triangle. SLIDE 2 SLIDE 3 36 people were asked to name their favorite dog. The results of the survey were as follows: Species Votes Labrador 16 Shepherd 10 Retriever 6 Other 4 Which of the following pie charts represents this information? SLIDE 4 SLIDE 5 The angle of a circle is 360� Find the angle marked X SLIDE 6 SLIDE 7 If we divide a circle into two halves, we get a semi-circle A line dividing a circle into two equal halves is called a diameter The angle of a straight line is 180� SLIDE 8 Find the missing angle SLIDE 9 SLIDE 10 A right-angle bisects the line and measures 90� Find the missing angle SLIDE 11 SLIDE 12 Work out the missing angle SLIDE 13 SLIDE 14 An acute angle is an angle between 0� and 90� A right-angle is 90� An obtuse angle is an angle between 90� and 180� A reflex angle is an angle between 180� and 360� SLIDE 15 Classify each angle SLIDE 16 SLIDE 17 The angle sum of a triangle Work out the missing angle x. SLIDE 18 SLIDE 19 Find the missing angles, x and y SLIDE 20 SLIDE 21 Find the angles A, B and C SLIDE 22 SLIDE 23 Triangles equilateral isosceles right-angled scalene three equal sides two equal sides no equal sides SLIDE 24 Find the angles a, b and c SLIDE 25 SLIDE 26 Find P SLIDE 27 SLIDE 28 Find the angles a, b and c SLIDE 29 SLIDE 30 Find x SLIDE 31 SLIDE 32 Find the angle x SLIDE 33 SLIDE 34 Angles that are vertically opposite each other are equal Find the angles a, b and c SLIDE 35 SLIDE36 Parallel lines remain always the same distance apart. Pairs of parallel lines are marked by arrows Corresponding angles in parallel are equal Find the angle x SLIDE 37 SLIDE 38 Alternating angles in parallel are equal Find x and y SLIDE 39 SLIDE 40 215 � 06 SLIDE 41 215 � 07 SLIDE 42 The figure is a regular hexagon Find the angles x and y SLIDE 43 SLIDE 44 The figure is a regular pentagon Find the angles x and y SLIDE 45 SLIDE 46 Find the exterior and interior angles of a regular octagon SLIDE 47 The exterior angle is 45� The interior angle is 135� SLIDE 48 The diagram shows two pairs of parallel lines. Find the angle x SLIDE 49 SLIDE 50 Find the angles a, b and c SLIDE 51 Angle a is The alternating angle on the other parallel line is also Within the triangle containing the angle we find the third angle as This gives b and c are alternating angles on a parallel, so